using OrdinaryDiffEq, DiffEqDevTools, Sundials, ModelingToolkit, ODEInterfaceDiffEq, Plots, DASSL, DASKR using LinearAlgebra @variables t y1(t)=1.0 y2(t)=2.0 y3(t)=3.0 @parameters p1=77.27 p2=8.375e-6 p3=0.161 D = Differential(t) eqs = [ D(y1) ~ p1*(y2+y1*(1-p2*y1-y2)) D(y2) ~ (y3-(1+y1)*y2)/p1 D(y3) ~ p3*(y1-y3) ] @named sys = ODESystem(eqs) simpsys = structural_simplify(sys) mmprob = ODEProblem(sys,[],(0.0,30.0)) daeprob = DAEProblem(sys,[D(y1)=>77.26935286375, D(y2)=>-0.012941633234114146, D(y3)=>-0.322],[],(0.0,30.0)) odaeprob = ODAEProblem(simpsys,[],(0.0,30.0)) ref_sol = solve(daeprob,IDA(),abstol=1/10^14,reltol=1/10^14); ode_ref_sol = solve(odaeprob,CVODE_BDF(),abstol=1/10^14,reltol=1/10^14); probs = [mmprob,daeprob,odaeprob] refs = [ref_sol,ref_sol,ode_ref_sol];
plot(ref_sol)
abstols = 1.0 ./ 10.0 .^ (6:9) reltols = 1.0 ./ 10.0 .^ (2:5); setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()), Dict(:prob_choice => 1, :alg=>Rodas4()), #Dict(:prob_choice => 1, :alg=>FBDF()), Dict(:prob_choice => 1, :alg=>QNDF()), Dict(:prob_choice => 1, :alg=>rodas()), Dict(:prob_choice => 1, :alg=>radau()), Dict(:prob_choice => 1, :alg=>RadauIIA5()), Dict(:prob_choice => 2, :alg=>DFBDF()), Dict(:prob_choice => 2, :alg=>IDA()), ] wp = WorkPrecisionSet(probs,abstols,reltols,setups;print_names=true, save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10) plot(wp)
Rosenbrock23 Rodas4 QNDF rodas radau RadauIIA5 DFBDF IDA
setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()), Dict(:prob_choice => 1, :alg=>Rodas4()), Dict(:prob_choice => 2, :alg=>IDA()), Dict(:prob_choice => 3, :alg=>Rosenbrock23()), Dict(:prob_choice => 3, :alg=>Rodas4()), Dict(:prob_choice => 3, :alg=>CVODE_BDF()), Dict(:prob_choice => 3, :alg=>TRBDF2()), Dict(:prob_choice => 3, :alg=>KenCarp4()), ] wp = WorkPrecisionSet(probs,abstols,reltols,setups; save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10) plot(wp)
abstols = 1.0 ./ 10.0 .^ (6:8) reltols = 1.0 ./ 10.0 .^ (2:4); setups = [Dict(:prob_choice => 3, :alg=>Rosenbrock23()), Dict(:prob_choice => 3, :alg=>Rodas4()), Dict(:prob_choice => 2, :alg=>IDA()), Dict(:prob_choice => 2, :alg=>DASSL.dassl()), Dict(:prob_choice => 2, :alg=>DASKR.daskr()), ] wp = WorkPrecisionSet(probs,abstols,reltols,setups; save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10) plot(wp)
abstols = 1.0 ./ 10.0 .^ (6:9) reltols = 1.0 ./ 10.0 .^ (2:5); setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()), Dict(:prob_choice => 1, :alg=>Rodas4()), #Dict(:prob_choice => 1, :alg=>FBDF()), # too slow Dict(:prob_choice => 1, :alg=>QNDF()), Dict(:prob_choice => 1, :alg=>rodas()), Dict(:prob_choice => 1, :alg=>radau()), Dict(:prob_choice => 1, :alg=>RadauIIA5()), Dict(:prob_choice => 2, :alg=>DFBDF()), Dict(:prob_choice => 2, :alg=>IDA()), ] gr() wp = WorkPrecisionSet(probs,abstols,reltols,setups;error_estimate = :l2, save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10) plot(wp)
abstols = 1.0 ./ 10.0 .^ (6:9) reltols = 1.0 ./ 10.0 .^ (2:5); setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()), Dict(:prob_choice => 1, :alg=>Rodas4()), Dict(:prob_choice => 2, :alg=>IDA()), Dict(:prob_choice => 3, :alg=>Rosenbrock23()), Dict(:prob_choice => 3, :alg=>Rodas4()), Dict(:prob_choice => 3, :alg=>CVODE_BDF()), Dict(:prob_choice => 3, :alg=>TRBDF2()), Dict(:prob_choice => 3, :alg=>KenCarp4()), ] wp = WorkPrecisionSet(probs,abstols,reltols,setups;error_estimate = :l2, save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10) plot(wp)
This is the speed at lower tolerances, measuring what's good when accuracy is needed.
abstols = 1.0 ./ 10.0 .^ (7:12) reltols = 1.0 ./ 10.0 .^ (4:9) setups = [Dict(:prob_choice => 1, :alg=>Rodas5()), Dict(:prob_choice => 3, :alg=>Rodas5()), Dict(:prob_choice => 1, :alg=>Rodas4()), Dict(:prob_choice => 3, :alg=>Rodas4()), #Dict(:prob_choice => 1, :alg=>FBDF()), Dict(:prob_choice => 1, :alg=>QNDF()), Dict(:prob_choice => 1, :alg=>rodas()), Dict(:prob_choice => 1, :alg=>radau()), Dict(:prob_choice => 1, :alg=>RadauIIA5()), Dict(:prob_choice => 2, :alg=>DFBDF()), Dict(:prob_choice => 2, :alg=>IDA()), ] gr() wp = WorkPrecisionSet(probs,abstols,reltols,setups; save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10) plot(wp)
wp = WorkPrecisionSet(probs,abstols,reltols,setups;error_estimate = :l2, save_everystep=false,appxsol=refs,maxiters=Int(1e5),numruns=10) plot(wp)
These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.
To locally run this benchmark, do the following commands:
using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/DAE","OregoDAE.jmd")
Computer Information:
Julia Version 1.6.5
Commit 9058264a69 (2021-12-19 12:30 UTC)
Platform Info:
OS: Linux (x86_64-pc-linux-gnu)
CPU: AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-11.0.1 (ORCJIT, znver2)
Environment:
BUILDKITE_PLUGIN_JULIA_CACHE_DIR = /cache/julia-buildkite-plugin
JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953
Package Information:
Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/DAE/Project.toml`
[165a45c3] DASKR v2.8.0
[e993076c] DASSL v2.6.0
[f3b72e0c] DiffEqDevTools v2.29.0
[961ee093] ModelingToolkit v8.3.2
[09606e27] ODEInterfaceDiffEq v3.10.1
[1dea7af3] OrdinaryDiffEq v6.6.3
[91a5bcdd] Plots v1.25.6
[31c91b34] SciMLBenchmarks v0.1.0
[c3572dad] Sundials v4.9.1
And the full manifest:
Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/DAE/Manifest.toml`
[1520ce14] AbstractTrees v0.3.4
[79e6a3ab] Adapt v3.3.3
[dce04be8] ArgCheck v2.1.0
[ec485272] ArnoldiMethod v0.2.0
[4fba245c] ArrayInterface v3.2.2
[15f4f7f2] AutoHashEquals v0.2.0
[198e06fe] BangBang v0.3.34
[9718e550] Baselet v0.1.1
[e2ed5e7c] Bijections v0.1.3
[62783981] BitTwiddlingConvenienceFunctions v0.1.1
[fa961155] CEnum v0.4.1
[2a0fbf3d] CPUSummary v0.1.6
[00ebfdb7] CSTParser v3.3.0
[d360d2e6] ChainRulesCore v1.11.6
[9e997f8a] ChangesOfVariables v0.1.2
[fb6a15b2] CloseOpenIntervals v0.1.4
[35d6a980] ColorSchemes v3.16.0
[3da002f7] ColorTypes v0.11.0
[5ae59095] Colors v0.12.8
[861a8166] Combinatorics v1.0.2
[a80b9123] CommonMark v0.8.5
[38540f10] CommonSolve v0.2.0
[bbf7d656] CommonSubexpressions v0.3.0
[34da2185] Compat v3.41.0
[b152e2b5] CompositeTypes v0.1.2
[a33af91c] CompositionsBase v0.1.1
[8f4d0f93] Conda v1.6.0
[187b0558] ConstructionBase v1.3.0
[d38c429a] Contour v0.5.7
[a8cc5b0e] Crayons v4.1.1
[165a45c3] DASKR v2.8.0
[e993076c] DASSL v2.6.0
[754358af] DEDataArrays v0.2.0
[9a962f9c] DataAPI v1.9.0
[864edb3b] DataStructures v0.18.11
[e2d170a0] DataValueInterfaces v1.0.0
[244e2a9f] DefineSingletons v0.1.2
[b429d917] DensityInterface v0.4.0
[2b5f629d] DiffEqBase v6.81.3
[459566f4] DiffEqCallbacks v2.20.1
[f3b72e0c] DiffEqDevTools v2.29.0
[c894b116] DiffEqJump v8.1.0
[77a26b50] DiffEqNoiseProcess v5.9.0
[163ba53b] DiffResults v1.0.3
[b552c78f] DiffRules v1.9.0
[b4f34e82] Distances v0.10.7
[31c24e10] Distributions v0.25.41
[ffbed154] DocStringExtensions v0.8.6
[5b8099bc] DomainSets v0.5.9
[7c1d4256] DynamicPolynomials v0.4.3
[da5c29d0] EllipsisNotation v1.3.0
[d4d017d3] ExponentialUtilities v1.11.0
[e2ba6199] ExprTools v0.1.8
[c87230d0] FFMPEG v0.4.1
[7034ab61] FastBroadcast v0.1.12
[9aa1b823] FastClosures v0.3.2
[1a297f60] FillArrays v0.12.7
[6a86dc24] FiniteDiff v2.10.0
[53c48c17] FixedPointNumbers v0.8.4
[59287772] Formatting v0.4.2
[f6369f11] ForwardDiff v0.10.25
[069b7b12] FunctionWrappers v1.1.2
[28b8d3ca] GR v0.63.1
[5c1252a2] GeometryBasics v0.4.1
[d7ba0133] Git v1.2.1
[86223c79] Graphs v1.5.1
[42e2da0e] Grisu v1.0.2
[cd3eb016] HTTP v0.9.17
[eafb193a] Highlights v0.4.5
[3e5b6fbb] HostCPUFeatures v0.1.5
[0e44f5e4] Hwloc v2.0.0
[7073ff75] IJulia v1.23.2
[615f187c] IfElse v0.1.1
[d25df0c9] Inflate v0.1.2
[83e8ac13] IniFile v0.5.0
[22cec73e] InitialValues v0.3.1
[8197267c] IntervalSets v0.5.3
[3587e190] InverseFunctions v0.1.2
[92d709cd] IrrationalConstants v0.1.1
[c8e1da08] IterTools v1.4.0
[42fd0dbc] IterativeSolvers v0.9.2
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.4.0
[682c06a0] JSON v0.21.2
[98e50ef6] JuliaFormatter v0.21.2
[ef3ab10e] KLU v0.2.3
[ba0b0d4f] Krylov v0.7.11
[0b1a1467] KrylovKit v0.5.3
[b964fa9f] LaTeXStrings v1.3.0
[2ee39098] LabelledArrays v1.7.0
[23fbe1c1] Latexify v0.15.9
[10f19ff3] LayoutPointers v0.1.4
[d3d80556] LineSearches v7.1.1
[7ed4a6bd] LinearSolve v1.11.0
[2ab3a3ac] LogExpFunctions v0.3.6
[bdcacae8] LoopVectorization v0.12.101
[1914dd2f] MacroTools v0.5.9
[d125e4d3] ManualMemory v0.1.6
[739be429] MbedTLS v1.0.3
[442fdcdd] Measures v0.3.1
[e9d8d322] Metatheory v1.3.3
[128add7d] MicroCollections v0.1.2
[e1d29d7a] Missings v1.0.2
[961ee093] ModelingToolkit v8.3.2
[46d2c3a1] MuladdMacro v0.2.2
[102ac46a] MultivariatePolynomials v0.4.2
[ffc61752] Mustache v1.0.12
[d8a4904e] MutableArithmetics v0.3.2
[d41bc354] NLSolversBase v7.8.2
[2774e3e8] NLsolve v4.5.1
[77ba4419] NaNMath v0.3.6
[8913a72c] NonlinearSolve v0.3.14
[54ca160b] ODEInterface v0.5.0
[09606e27] ODEInterfaceDiffEq v3.10.1
[6fe1bfb0] OffsetArrays v1.10.8
[429524aa] Optim v1.6.0
[bac558e1] OrderedCollections v1.4.1
[1dea7af3] OrdinaryDiffEq v6.6.3
[90014a1f] PDMats v0.11.5
[d96e819e] Parameters v0.12.3
[69de0a69] Parsers v2.2.0
[ccf2f8ad] PlotThemes v2.0.1
[995b91a9] PlotUtils v1.1.3
[91a5bcdd] Plots v1.25.6
[e409e4f3] PoissonRandom v0.4.0
[f517fe37] Polyester v0.6.3
[1d0040c9] PolyesterWeave v0.1.2
[85a6dd25] PositiveFactorizations v0.2.4
[d236fae5] PreallocationTools v0.2.3
[21216c6a] Preferences v1.2.3
[1fd47b50] QuadGK v2.4.2
[74087812] Random123 v1.4.2
[e6cf234a] RandomNumbers v1.5.3
[3cdcf5f2] RecipesBase v1.2.1
[01d81517] RecipesPipeline v0.5.0
[731186ca] RecursiveArrayTools v2.24.1
[f2c3362d] RecursiveFactorization v0.2.8
[189a3867] Reexport v1.2.2
[42d2dcc6] Referenceables v0.1.2
[05181044] RelocatableFolders v0.1.3
[ae029012] Requires v1.3.0
[ae5879a3] ResettableStacks v1.1.1
[79098fc4] Rmath v0.7.0
[47965b36] RootedTrees v1.2.1
[7e49a35a] RuntimeGeneratedFunctions v0.5.3
[3cdde19b] SIMDDualNumbers v0.1.0
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.28
[1bc83da4] SafeTestsets v0.0.1
[0bca4576] SciMLBase v1.26.0
[31c91b34] SciMLBenchmarks v0.1.0
[6c6a2e73] Scratch v1.1.0
[efcf1570] Setfield v0.8.1
[992d4aef] Showoff v1.0.3
[699a6c99] SimpleTraits v0.9.4
[b85f4697] SoftGlobalScope v1.1.0
[a2af1166] SortingAlgorithms v1.0.1
[47a9eef4] SparseDiffTools v1.20.0
[276daf66] SpecialFunctions v2.0.0
[171d559e] SplittablesBase v0.1.14
[aedffcd0] Static v0.4.1
[90137ffa] StaticArrays v1.3.3
[82ae8749] StatsAPI v1.2.0
[2913bbd2] StatsBase v0.33.14
[4c63d2b9] StatsFuns v0.9.15
[7792a7ef] StrideArraysCore v0.2.9
[69024149] StringEncodings v0.3.5
[09ab397b] StructArrays v0.6.4
[c3572dad] Sundials v4.9.1
[d1185830] SymbolicUtils v0.19.7
[0c5d862f] Symbolics v4.3.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.6.1
[8ea1fca8] TermInterface v0.2.3
[8290d209] ThreadingUtilities v0.4.7
[ac1d9e8a] ThreadsX v0.1.9
[a759f4b9] TimerOutputs v0.5.15
[0796e94c] Tokenize v0.5.21
[28d57a85] Transducers v0.4.68
[a2a6695c] TreeViews v0.3.0
[d5829a12] TriangularSolve v0.1.9
[5c2747f8] URIs v1.3.0
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.10.1
[41fe7b60] Unzip v0.1.2
[3d5dd08c] VectorizationBase v0.21.23
[81def892] VersionParsing v1.3.0
[19fa3120] VertexSafeGraphs v0.2.0
[44d3d7a6] Weave v0.10.10
[ddb6d928] YAML v0.4.7
[c2297ded] ZMQ v1.2.1
[700de1a5] ZygoteRules v0.2.2
[6e34b625] Bzip2_jll v1.0.8+0
[83423d85] Cairo_jll v1.16.1+1
[655fdf9c] DASKR_jll v1.0.0+0
[5ae413db] EarCut_jll v2.2.3+0
[2e619515] Expat_jll v2.2.10+0
[b22a6f82] FFMPEG_jll v4.4.0+0
[a3f928ae] Fontconfig_jll v2.13.93+0
[d7e528f0] FreeType2_jll v2.10.4+0
[559328eb] FriBidi_jll v1.0.10+0
[0656b61e] GLFW_jll v3.3.5+1
[d2c73de3] GR_jll v0.63.1+0
[78b55507] Gettext_jll v0.21.0+0
[f8c6e375] Git_jll v2.34.1+0
[7746bdde] Glib_jll v2.68.3+2
[3b182d85] Graphite2_jll v1.3.14+0
[2e76f6c2] HarfBuzz_jll v2.8.1+1
[e33a78d0] Hwloc_jll v2.7.0+0
[aacddb02] JpegTurbo_jll v2.1.0+0
[c1c5ebd0] LAME_jll v3.100.1+0
[dd4b983a] LZO_jll v2.10.1+0
[e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.8.7+0
[7e76a0d4] Libglvnd_jll v1.3.0+3
[7add5ba3] Libgpg_error_jll v1.42.0+0
[94ce4f54] Libiconv_jll v1.16.1+1
[4b2f31a3] Libmount_jll v2.35.0+0
[89763e89] Libtiff_jll v4.3.0+0
[38a345b3] Libuuid_jll v2.36.0+0
[c771fb93] ODEInterface_jll v0.0.1+0
[e7412a2a] Ogg_jll v1.3.5+1
[458c3c95] OpenSSL_jll v1.1.13+0
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[91d4177d] Opus_jll v1.3.2+0
[2f80f16e] PCRE_jll v8.44.0+0
[30392449] Pixman_jll v0.40.1+0
[ea2cea3b] Qt5Base_jll v5.15.3+0
[f50d1b31] Rmath_jll v0.3.0+0
[fb77eaff] Sundials_jll v5.2.0+1
[a2964d1f] Wayland_jll v1.19.0+0
[2381bf8a] Wayland_protocols_jll v1.23.0+0
[02c8fc9c] XML2_jll v2.9.12+0
[aed1982a] XSLT_jll v1.1.34+0
[4f6342f7] Xorg_libX11_jll v1.6.9+4
[0c0b7dd1] Xorg_libXau_jll v1.0.9+4
[935fb764] Xorg_libXcursor_jll v1.2.0+4
[a3789734] Xorg_libXdmcp_jll v1.1.3+4
[1082639a] Xorg_libXext_jll v1.3.4+4
[d091e8ba] Xorg_libXfixes_jll v5.0.3+4
[a51aa0fd] Xorg_libXi_jll v1.7.10+4
[d1454406] Xorg_libXinerama_jll v1.1.4+4
[ec84b674] Xorg_libXrandr_jll v1.5.2+4
[ea2f1a96] Xorg_libXrender_jll v0.9.10+4
[14d82f49] Xorg_libpthread_stubs_jll v0.1.0+3
[c7cfdc94] Xorg_libxcb_jll v1.13.0+3
[cc61e674] Xorg_libxkbfile_jll v1.1.0+4
[12413925] Xorg_xcb_util_image_jll v0.4.0+1
[2def613f] Xorg_xcb_util_jll v0.4.0+1
[975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
[c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
[35661453] Xorg_xkbcomp_jll v1.4.2+4
[33bec58e] Xorg_xkeyboard_config_jll v2.27.0+4
[c5fb5394] Xorg_xtrans_jll v1.4.0+3
[8f1865be] ZeroMQ_jll v4.3.4+0
[3161d3a3] Zstd_jll v1.5.0+0
[0ac62f75] libass_jll v0.15.1+0
[f638f0a6] libfdk_aac_jll v2.0.2+0
[b53b4c65] libpng_jll v1.6.38+0
[a9144af2] libsodium_jll v1.0.20+0
[f27f6e37] libvorbis_jll v1.3.7+1
[1270edf5] x264_jll v2021.5.5+0
[dfaa095f] x265_jll v3.5.0+0
[d8fb68d0] xkbcommon_jll v0.9.1+5
[0dad84c5] ArgTools
[56f22d72] Artifacts
[2a0f44e3] Base64
[ade2ca70] Dates
[8bb1440f] DelimitedFiles
[8ba89e20] Distributed
[f43a241f] Downloads
[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[b27032c2] LibCURL
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions
[44cfe95a] Pkg
[de0858da] Printf
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays
[10745b16] Statistics
[4607b0f0] SuiteSparse
[fa267f1f] TOML
[a4e569a6] Tar
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll
[deac9b47] LibCURL_jll
[29816b5a] LibSSH2_jll
[c8ffd9c3] MbedTLS_jll
[14a3606d] MozillaCACerts_jll
[4536629a] OpenBLAS_jll
[05823500] OpenLibm_jll
[efcefdf7] PCRE2_jll
[bea87d4a] SuiteSparse_jll
[83775a58] Zlib_jll
[8e850ede] nghttp2_jll
[3f19e933] p7zip_jll